Whole heart action potential duration restitution properties in cardiac patients: a combined clinical and modelling study

Exp Physiol 91.2 pp 339–354 339

Experimental Physiology – Modelling of Biological Systems

Whole heart action potential duration restitutionproperties in cardiac patients: a combined clinicaland modelling study

Martyn P. Nash1, Chris P. Bradley2, Peter M. Sutton3, Richard H. Clayton4, Panny Kallis3,

Martin P. Hayward3, David J. Paterson2 and Peter Taggart3

1Bioengineering Institute and Engineering Science, University of Auckland, New Zealand2Burdon Sanderson Cardiac Science Centre, Department of Physiology, Anatomy & Genetics, University of Oxford, UK3Departments of Cardiology and Cardiothoracic Surgery, University College Hospital, London, UK4Department of Computer Science, University of Sheffield, UK

Steep action potential duration (APD) restitution has been shown to facilitate wavebreak

and ventricular fibrillation. The global APD restitution properties in cardiac patients are

unknown. We report a combined clinical electrophysiology and computer modelling study

to: (1) determine global APD restitution properties in cardiac patients; and (2) examine the

interaction of the observed APD restitution with known arrhythmia mechanisms. In 14 patients

aged 52–85 years undergoing routine cardiac surgery, 256 electrode epicardial mapping was

performed. Activation–recovery intervals (ARI; a surrogate for APD) were recorded over the

entire ventricular surface. Mono-exponential restitution curves were constructed for each

electrode site using a standard S1–S2 pacing protocol. The median maximum restitution slope

was 0.91, with 27% of all electrode sites with slopes < 0.5, 29% between 0.5 and 1.0, and 20%

between 1.0 and 1.5. Eleven per cent of restitution curves maintained slope > 1 over a range

of diastolic intervals of at least 30 ms; and 0.3% for at least 50 ms. Activation–recovery interval

restitution was spatially heterogeneous, showing regional organization with multiple discrete

areas of steep and shallow slope. We used a simplified computer model of 2-D cardiac tissue to

investigate how heterogeneous APD restitution can influence vulnerability to, and stability of

re-entry. Our model showed that heterogeneity of restitution can act as a potent arrhythmogenic

substrate, as well as influencing the stability of re-entrant arrhythmias. Global epicardial mapping

in humans showed that APD restitution slopes were organized into regions of shallow and steep

slopes. This heterogeneous organization of restitution may provide a substrate for arrhythmia.

(Received 31 October 2005; accepted after revision 10 January 2006; first published online 1 February 2006)

Corresponding author P. Taggart: Departments of Cardiology and Cardiothoracic Surgery, University College Hospital,

16–18 Westmoreland Street, London W1G 8PH, UK. Email: [email protected]

Sudden cardiac death due to arrhythmia continues to posea major health problem. Despite substantial progress, theresults of pharmacological intervention have so far proveddisappointing (Anon, 1992; Tan, 1996). This may be duein part to the paucity of information presently available onthe relevant basic electrophysiology of the human heart insitu. The acquisition of such data is of necessity limitedby constraints inherent in studies in humans. However,interpretation may be enhanced by combining such studieswith computer modelling. We report studies in patientswith heart disease in which we have characterized basic

electrophysiological properties known to be relevant toarrhythmogenesis, together with a preliminary study usinga computational model of 2-D cardiac tissue in whichwe have tested how these properties may interact withmechanisms of arrhythmogenesis.

The spatial dispersion of action potential duration(APD) is known to play a major role in arrhythmogenesis(Han & Moe, 1964; Kuo et al. 1983; Sampson & Henriquez,2001; Xie et al. 2001a). Several disease processes arecommonly associated with increased spatial dispersionof repolarization, including coronary artery disease and

C© 2006 The Authors. Journal compilation C© 2006 The Physiological Society DOI: 10.1113/expphysiol.2005.031070

340 M. P. Nash and others Exp Physiol 91.2 pp 339–354

ventricular hypertrophy (Janse & Wit, 1989). Recentattention has focused on the dynamic modulation ofAPD by an abrupt change in cycle length referred to asrestitution (Boyett & Jewell, 1978). When the restitutioncurve relating APD to the preceding diastolic interval(DI) has a steep slope (i.e. greater than unity), successivechanges in cycle length at a fast rate may induce oscillationsin APD (Nolasco & Dahlen, 1968). It has been shownexperimentally that steep APD restitution may facilitatewavebreak and fibrillation (Karma, 1994; Gilmour &Chialvo, 1999; Weiss et al. 1999), whereas reducing theslope may prevent or terminate fibrillation (Garfinkelet al. 2000). Whether restitution in the human heart issteep enough to sustain multiple wavebreak mechanismsof ventricular fibrillation (VF) has been questioned on thebasis of the available data, which have been limited to asmall number of single or paired site recordings (Franzet al. 1988; Morgan et al. 1992; Taggart et al. 2003).

In addition to the steepness of the APD restitutioncurve, spatial heterogeneity of restitution slopes is thoughtto be important (Laurita et al. 1996, 1998; Sampson& Henriquez, 2001; Xie et al. 2001a; Banville & Gray,2002; Fenton et al. 2002) through several mechanisms,including the promotion of the coexistence of multiplespiral waves (Xie et al. 2001b), enhancment of oscillationsof refractoriness (Watanabe et al. 2001) and creationof discordant alternans (Laurita et al. 1996; Pastoreet al. 1999). Discordant alternans occurs when the steepportion of the restitution curves in adjacent regions cross,resulting in a reversal of voltage gradient on alternatebeats. Calcium cycling and cellular calcium accumulationhave been shown to modulate APD restitution andalternans, so regional heterogeneities of calcium dynamicsare likely to be important (Goldhaber et al. 2005).However, the spatial dispersion of APD restitution inhumans is at present unknown and usually assumeshomogeneous restitution or a smooth apex-to-basegradient, as present in some animal models (Rosenbaumet al. 1991; Laurita et al. 1996). Our unpublished pilotobservations in humans have suggested that restitutionmay be markedly heterogeneous, which underlines theneed for global assessment of restitution properties intypical patient groups. Subsequent to these pilot studies,a recent modelling study has provided further theoreticalevidence that heterogeneous restitution can form a potentarrhythmogenic substrate (Clayton & Taggart, 2005).

Methods

Patients

We studied 14 patients aged 52–85 years (mean 67;11 males) undergoing routine cardiac surgical procedures.The study was approved by the local hospital ethicscommittee, and written informed consent was obtained

from all patients prior to the study. The protocolscomply with the Declaration of Helsinki. Individualpatient details are given in Tables 1 and 2. Eight patientswere undergoing graft procedures for coronary arterydisease. Six patients were undergoing replacement surgeryfor aortic valve disease and had no haemodynamicallysignificant coronary artery disease (defined as greaterthan 50% stenosis in any one major vessel). The patientgroups were at low risk of ventricular tachycardia (VT)/VF(Sanders et al. 2005); none had a history of arrhythmia orsyncopal episodes; left ventricular ejection fraction wasnormal in all patients; and only two subjects had previousmyocardial infarction. Routine medication was continueduntil approximately 15 h prior to surgery.

Electrical imaging

Following cannulation for cardiopulmonary bypass(but prior to its commencement), a sock containing256 unipolar contact electrodes (interelectrode spacingapproximately 10 mm) spanning the entire left and rightventricles was fitted over the epicardium. As previouslydescribed (Nash et al. 2001, 2003), unipolar epicardialelectrograms were sampled at 1 kHz using a UnEmapsystem (Auckland UniServices Ltd, New Zealand), andconventional signal analysis techniques were used toobtain epicardial activation–recovery intervals (ARI) as asurrogate for APD (Haws & Lux, 1990). Bipolar ventricularpacing was established from two sock electrodes at twicediastolic threshold using a 2 ms pulse duration. A basiccycle length (BCL) of 600 ms was chosen when possible(9 patients), but in five patients a shorter basic cycle(between 450 and 550 ms) was necessary to ensure capture,owing to a faster intrinsic heart rate. The pacing siteswere: coronary artery disease (CAD), 4 mid-left ventricle(LV), 2 mid-LV/right ventricle (RV) border, 1 mid-RV,1 apex; and aortic valve disease (AVD), 4 mid-LV, 2 apex.Following each train of nine steady-state S1 stimuli at theBCL, a shorter interval S2 stimulus was interposed. TheS1–S2 interval was decremented by 50 ms steps to 400 ms;then by 20 ms steps to 340 ms; and then by 5 ms intervalsuntil loss of ventricular capture.

Estimating APD restitution using ARI

The ARI is an established (Haws & Lux, 1990)and now widely used surrogate for APD and APDrestitution. In pilot studies (unpublished observations), wecompared restitution curves obtained using monophasicaction potential (MAP) and ARI recordings from thesame epicardial site in humans, which confirmed theapplicability of the technique in the setting of patientsundergoing cardiac surgery. A recent study using non-contact mapping of the endocardium in humans (Yueet al. 2004) has shown that for complexes with upright

C© 2006 The Authors. Journal compilation C© 2006 The Physiological Society

Exp Physiol 91.2 pp 339–354 Whole heart APD restitution properties in cardiac patients 341

Table 1. Patient characteristics

Age/Gender BCL LMS LAD Cx RCA EF MI β-Block Ca2+ block ACE

CAD53 male 600 N mod S mod 74 — Yes Yes —58 male 600 N S S mod 74 — Yes — Yes68 female 600 N mild S blocked 58 — Yes — Yes71 male 600 N blocked N S 60 — Yes Yes —60 male 520 N S mod mod 72 Yes — Yes —59 female 550 N mod S mod 57 — — Yes Yes59 male 600 N S mod mod 62 Yes Yes — Yes74 male 600 mild N N N 65 — — Yes —

AVD75 male 480 N N N N 76 — — — Yes70 male 600 N N N N 75 — Yes — —52 male 600 N N N N 71 — — — Yes73 female 450 N N N N 63 — — — Yes85 male 550 N N N N 70 — — — Yes82 male 600 N N N N 58 — — — Yes

Abbreviations: CAD, coronary artery disease; AVD, aortic valve disease; and BCL, basic paced cycle length (ms). Coronary arteries: LMS,left main stem; LAD, left anterior descending; Cx, circumflex; and RCA, right coronary artery. N, no haemodynamically significantstenosis (i.e. < 50% narrowing); mild, 50–70% stenosis; mod, moderate, 70–90% stenosis; and S, severe, > 90% stenosis. EF, ejectionfraction(%); and MI, previous myocardial infarction. Medication: β-Block, β-blockade; Ca2+ block, calcium antagonists; and ACE, ACEinhibitors.

Table 2. Additional data for AVD patients

Age/Gender LVDd LVDs LVPWd IVSd Ao grad AR

75 male 5.4 3.4 1.3 1.3 50 No70 male 4.9 3.7 1.3 1.7 88 1/452 male 5.1 3.2 1.2 1.1 70 1/473 female 6.1 4.0 0.9 0.8 85 1/485 male 4.6 3.6 1.1 1.1 60 No82 male 5.9 3.7 1.0 1.1 75 No

Left ventricular dimensions: LVDd (cm), left ventricle, enddiastole; LVDs (cm), left ventricle, end systole; LVPWd (cm), leftventricular posterior wall, end diastole; IVSd (cm), interventricularseptum, end diastole; Ao, aortic gradient (mmHg); and AR, aorticregurgitation (grade).

T waves, a closer correlation was obtained between ARIand MAP duration (measured at 90% repolarization)when ARI was measured to the steepest downstroke of theT wave (‘alternative method’), rather than the standard(Wyatt) method of measuring the ARI to the steepestupstroke of the T wave (Haws & Lux, 1990). We comparedARIs and restitution curves computed using the standardmethod against the alternative method. The alternativemethod yielded ARI values that were longer by 74 ± 10 ms(mean ± s.d.), but exerted only minimal influence onthe resulting restitution slopes and spatial distributionsof restitution properties (data not shown). The standard(Wyatt) method of calculating ARI was used throughoutthe present study.

Restitution analysis

Only signals with good quality signal-to-noise ratioswere accepted. From the 256 electrode sites, good qualityelectrograms suitable for analysis were obtained with

an overall mean ± s.d. of 206 ± 45 signals per patient.Standard restitution curves for ARI versus DI wereconstructed for each individual electrode site using a least-squares fit to the mono-exponential function:

ARI = ARISS − a exp(−DI/b) (1)

where the steady-state ARI (ARISS), a and b are theparameters of the fit. Given this relationship, the maximumrestitution slope is given by:

Smax = (a/b) exp(−DImin/b) (2)

where DImin is the minimum non-refractory DI. The rangeof DIs for which the slope is steeper than a specified value(e.g. Scrit = 1) is given by:

DIrange = −b ln(Scrit[b/a]) − DImin (3)

These quantities are related by:

DIrange = b ln(Smax/Scrit) (4)

It is noteworthy that a recent study in humans comparingrestitution properties obtained using the standard S1–S2protocol and a dynamic protocol obtained largely similarresults (Pak et al. 2004).

Statistical analysis

The statistical model used for analysis throughout thispaper was a linear mixed model. The fixed factors were apathology group (CAD versus AVD), an apex–base group(apex versus base) and a left–right group (LV versus RV).All electrodes were designated as either apical or basal,



and either LV or RV, according to their epicardial location.The interactions of pathology∗apex–base, pathology∗left–right and apex–base∗left–right were included in the modelonly if the main effects were significant. The multipleelectrode measurements made for each patient formedthe random effect for the analysis. For situations wherenon-normal data prevented direct application of the linearmixed model, a non-parametric Mann–Whitney U testwas used to test for significance of a group. The analysis wasperformed using the SPSS statistical package (SPSS 13.0 forWindows).

Computational model

We examined the implications of heterogeneous APDrestitution for the initiation and stability of re-entrantarrhythmias using a simplified model of 2-D cardiactissue. Action potential propagation was described by themonodomain equation:

∂Vm

∂t= D

(∂2Vm

∂x2+ ∂2Vm

∂y2

)−

(1

Cm

)Iion (5)

where V m denotes transmembrane voltage, Cm specificmembrane capacitance, D a diffusion coefficient, and I ion

current flow though the cell membrane per unit area. Forsimplicity, and to enable us to easily manipulate APDrestitution, we chose to use a simplified model of thecardiac cell membrane (to give I ion) as developed by Fentonand Karma. This model has three variables and is describedin detail elsewhere (Fenton & Karma, 1998; Clayton &Holden, 2002; Fenton et al. 2002; Clayton & Taggart, 2005).We used the parameter sets given in Table 3 to give twovariants of the model designated Steep1 and Steep2, eachwith different APD restitution.

Table 3. Parameter values for each variant of the three-variableFenton–Karma model. Parameters are defined in detail elsewhere(Fenton & Karma, 1998; Clayton & Holden, 2002; Fenton et al.2002; Clayton & Taggart, 2005)

Parameter Steep1 Steep2 Units

V0 −85 −85 mVVfi 15 15 mVgfi 4 4 mS cm−2

td 0.25 0.25 mstr 33 50 mstsi 30 45 mst0 12.5 8.3 mstv

+ 3.33 3.33 mstv1

− 1250 1000 mstv

2− 19.6 19.2 mstw

+ 870 667 mstw

− 41 11 msuc 0.13 0.13 Noneuv 0.04 0.055 Noneuc

si 0.85 0.85 Nonek 10 10 None

We solved the model equations using a simple explicitEuler scheme, and the non-linear diffusion equationusing a forward-time centred-space finite differencemethod with a time step (�t) of 0.1 ms, a space step(�x) of 0.25 mm, and no-flux boundary conditions ateach external edge. The specific membrane capacitancewas set to 1 μF cm−2, and the diffusion coefficientset to 0.1 mm2 ms−1. We observed only small (< 1%)changes in conduction velocity for time steps of 0.8and 0.12 ms, indicating that the numerical scheme wasstable.

We examined the initiation and stability of re-entryin several 150 × 150 mm 2-D tissue models, each witha circular region at the centre being assigned Steep2restitution, and the surrounding tissue assigned Steep1restitution. The circular region was varied in size by settingthe radius to 12.5, 25 or 50 mm. We studied the initiationof re-entry by setting the tissue to a resting state, andpacing from the bottom edge. We studied the stability ofre-entry by imposing an Archimedean spiral as the initialcondition.

Results

Restitution curves

The overall mean ± s.e.m. steady-state ARI was 242 ± 6 msacross all patients. The maximum restitution slopesspanned a wide range. Figure 1A shows the distribution ofslopes ranging from shallow to steep. The standard (Wyatt)and alternative methods of determining ARI yieldedslope distributions with good overall correspondence(Fig. 1B). The mean ± s.e.m. maximum slope for allpatients was 1.1 ± 0.02 (median 0.9, range 0.0–5.6), with55% of electrodes having slopes below 1, 20% having slopesbetween 1 and 1.5, and 13% having slopes above 2. A slopethat is steep over a greater length of the rising portion ofthe restitution curve is thought to be more proarrhythmicthan a slope of comparable steepness, but that is steepover only a short length of the curve (Qu et al. 1999). Wetherefore evaluated the range of diastolic intervals overwhich slopes steeper than 1 remained steeper than 1. Forthe 45% of electrode sites with slopes steeper than 1, only11% were maintained steeper than 1 over a DI range of atleast 30 ms, and only 0.3% of sites over a DI range of at least50 ms.

LV–RV and apex–base comparisons

The mean ± s.e.m. maximum restitution slopes wereslightly steeper over the LV (1.19 ± 0.03; median 0.98;range 0.0–5.6) compared to the RV (1.03 ± 0.02;median 0.83; range 0.0–5.03), as illustrated in Fig. 2A.The distribution of restitution slopes was non-normal(as shown in Fig. 1), so standard statistical tests could



0

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20

30

40

0.0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-3.5 3.5-4.0 >4.0

Restitution slope range

Mean

pro

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Restitution slope range

Pro

po

rtio

n o

f ele

ctr

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es (

%) ARI (Wyatt)

ARI (Alte rna tive )

Figure 1. Restitution slope distributionA, the distribution of maximum restitutionslopes is shown as the proportion ofelectrodes with slopes within a series ofranges spanning from shallow restitution(left) to steep restitution (right). Overall,55% of slopes were less than 1 and 13%above 2. B, distribution of restitution slopesin one patient measured using the standard(Wyatt) method of determining ARI (to thesteepest upstroke of the T wave), and bythe alternative method (for uprightT waves, measured to the steepestdownstroke of the T wave), showing agood overall correspondence in the resultsobtained by the two methods.

not be applied. However, a non-parametric testshowed a significant difference in the restitution slopebetween the LV and RV (P < 0.001 non-parametric).Apex and base slopes were relatively similar inmagnitude, i.e. apex 1.12 ± 0.02 (median 0.94; range 0.0–5.54) compared to the base 1.10 ± 0.03 (median 0.84;range 0.0–5.6; P < 0.01 non-parametric).

Comparison of CAD and AVD patient groups

Restitution was shallower in the CAD group compared tothe AVD group (Fig. 2B). The overall mean ± s.e.m. slopeswere: CAD 1.0 ± 0.02 (median 0.83, range 0.0–4.88); andAVD 1.2 ± 0.03 (median 0.96, range 0.0–5.7; P < 0.001non-parametric). The amplitude of the restitution curvewas measured as the range of ARIs between that at

0.00

0.50

1.00

LV RV

Me

an

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x R

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titu

tio

n S

lop

e

0.00

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1.00

AVD CAD

Me

an

Ma

x R

es

titu

tio

n S

lop

e

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AVD CAD

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an

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sti

tuti

on

Am

plitu

de

(m

s)

ARI

400 ms

Resti

tuti

on

Am

plitu

de

Cycle length

A B

C

Figure 2. Restitution properties byregion and pathologyA The mean maximum restitution slopecalculated over all LV electrodes was steeperthan that for all RV electrodes (P < 0.001non-parametric). B Mean restitution slopesfor the CAD and AVD patients showingflatter restitution in the CAD patients(P < 0.001 non-parametric). C Theamplitude of the restitution curves wasmeasured as the range of ARIs between theminimum S2 value and the S2 value at anS1-S2 coupling interval of 400 ms, asillustrated by the dashed lines in theschematic (right). The mean restitutionamplitude was shallower for the CAD groupcompared to the AVD group (P < 0.05).AVD: aortic valve disease group; CAD:coronary artery disease group. Error barsshow standard errors.

the shortest non-refractory S1–S2 coupling interval, andthe ARI at an S1–S2 interval of 400 ms (see Fig. 2C).Again consistent with flatter restitution in the CADpatients, the restitution amplitude was substantially lowerin this patient group compared to the AVD patients(CAD 38 ± 5 ms; AVD 56 ± 6 ms; P < 0.05).

Spatial organization of restitution

The spatial distribution of the maximum restitutionslope in the patients we studied was heterogeneous.The distribution was not random, but exhibited regionalorganization, resulting in multiple gradients over theepicardium between areas of steep slope and areas ofshallower slope (Fig. 3). Figure 3A shows examples fromfour patients, illustrating the wide range of restitution





slopes and the juxtaposition of large areas of steepslopes with areas of shallower slopes. These regions ofdifferent slope were separated by spatial gradients, whichare illustrated in Fig. 3B with contours of equal slope.A similar pattern pertains with regard to the portion ofthe restitution curve over which a steep curve remainssteep before flattening to approach its asymptote (seeinset in Fig. 3B). This parameter (so-called ‘DI range’,quantifying the range of diastolic intervals over which therestitution slope is > 1), was also regionally organizedwith a similar spatial pattern to the associated maximumrestitution slope distribution. This was expected, giventhe mathematical relationship between DI range andmaximum slope as detailed in the Methods section(Equation (4)).

Examples of restitution gradients are illustrated in Figs 4and 5. Figure 4 illustrates a grouping of restitution curvesspanning an area of approximately 5 cm × 5 cm, in whichthere was a central region of relatively steep restitution,with gradients of progressively flatter restitution towardsthe periphery. Figure 5 shows a region in a different patient,illustrating the opposite pattern. In this case, the centralzone had relatively flat restitution and was surrounded bysteeper restitution towards the periphery.

ARI dispersion

As a measure of ARI dispersion, the coefficient of variation(COV = standard deviation as a percentage of the mean)was found to be substantially greater at shorter DIs(Fig 6A). Similar results in animal models have beenattributed to the shape of the restitution curve. Toinvestigate this notion, ARIs following short diastolicintervals in the range of 0–100 ms were subdividedaccording to the steepness of their restitution curves.A positive correlation with a regression coefficient of2.44 ± 0.56 (P < 0.001) was present between dispersionof repolarization (COV of ARI) and the steepness of therestitution slope (Fig. 6B).

Computational model

The model geometry, APD and conduction velocity (CV)restitution for each model variant are shown in Fig. 7. Inthis study, we investigated the potential arrhythmogenicinfluence of a region of steep APD restitution (Steep2,

Figure 3. Case studies illustrating spatial heterogeneities of restitution propertiesA, case studies from four patients, two with aortic valve disease (AVD) and two with coronary artery disease (CAD),illustrating the heterogeneity of maximum restitution slope within and between patients. B, spatial organizationof maximum restitution slope (left) and range of diastolic intervals (DI range; see inset for definition) for whichrestitution slope was greater than 1 (right) in two patients, illustrating the regional heterogeneity within patientsand between patients. Data are illustrated using a 3-D representation of the ventricular epicardial surface, and theextrema of the blue–white–red spectra are indicated separately for each map (blue, minimum; red, maximum).The inset demonstrates the calculation of the DI range for each electrode site.

relatively long APD at short DI) located within a region ofshallower APD restitution (Steep1, relatively short APDat short DI). We found that we could readily initiatewavebreak and re-entry in this model with an S1–S2–S3stimulus protocol (see Fig. 8) and with this combination ofrestitution properties. Using an S1–S2 interval of 200 ms,we were able to initiate wavebreak and re-entry for S2–S3intervals of between 102 and 158 ms for a radius of 50 mm,and between 102 and 153 ms for a radius of 12.5 mm.Figure 8 shows an illustrative example for a radius of50 mm, an S1–S2 interval of 200 ms, and an S2–S3 intervalof 120 ms.

Figure 8A shows a sequence of snapshots during pacingof the model tissue with an S1–S2–S3 protocol. Eachsnapshot shows the transmembrane voltage encoded as agreyscale with depolarized regions in white and repolarizedregions in black. The tissue inside the dashed grey circle wasassigned Steep2 restitution, whilst the surrounding tissuewas assigned Steep1 restitution. Stimuli were given alongthe bottom edge of the model, and initiated propagatingaction potentials. The first snapshot shows these actionpotentials 400 ms after the S1 stimulus was given. By thistime the S1 action potential has propagated to the top ofthe simulated tissue. The S2 stimulus was closely coupled,and the action potential was prolonged in the circularregion with Steep2 restitution. Figure 8B shows the APDrestitution data for these two regions. The dashed lines inFig. 8B indicate the APD of the action potentials elicitedin each region by the S2 stimulus. Figure 8C shows theaction potentials elicited in the Steep2 (top trace) andSteep1 regions (bottom trace). The relatively long actionpotential in the Steep2 region results in block of the S3action potential, and this leads to wavebreak and ultimatelyto spiral wave re-entry. In a comprehensive study of theinitiation of wavebreak and re-entry by this mechanism(Clayton & Taggart, 2005), we found a wide range of S1–S2–S3 intervals that could initiate re-entry in this typeof model, with different configurations of heterogeneity.We also found that this mechanism resulted in wavebreakfor models with steep (slope > 1) and shallow (slope < 1)APD restitution.

Heterogeneous APD restitution may also play a rolein the stability of arrhythmias, as well as their initiation(an illustrative example is shown in Fig. 9). Both Steep1and Steep2 variants of our model had steep (slope > 1)





APD restitution, and the Steep1 variant was associatedwith unstable re-entry, consistent with the restitutionhypothesis (Fig. 9A). However, although the Steep2 variantpossessed steep APD restitution at very short DI, the DIrange for steep slopes was substantially smaller than theSteep1 variant. Thus, during re-entry, curvature effectsprevented these values of DI from being achieved, andso re-entry was stable despite the steep APD restitution(Fig. 9B).

We found that re-entry in our model of heterogeneousAPD restitution was unstable if the tip of the re-entrantwave moved into a region described by Steep1 APDrestitution, provided that this region was large enoughfor the instability to develop. Figure 9C shows an examplewhere the circular region had Steep1 APD restitution witha radius of 50 mm, and the rest of the tissue had Steep2restitution. Initiation of a re-entrant wave with its tiplocated at the centre of this region resulted in instabilityas shown. Reducing the radius of the region with Steep1restitution from 50 to 12.5 mm prevented the instabilityfrom developing, as shown in Fig. 9D.

Discussion

Multi-electrode mapping of ARIs over the entire left andright ventricular epicardium was performed in cardiacpatients in order to characterize the global APD restitutionproperties. Our findings are consistent with those ofYue et al. (2005) for the human endocardium, butdiffer from other reported models in that restitutionwas neither homogeneous nor were smooth apex-to-base gradients present. Our findings also agree withthose of Yue et al. (2005) in showing non-uniformitybetween LV and RV restitution slopes. The observedheterogeneities were organized into regions with multiplegradients between areas of steeper slope and areas ofshallower slope. The range of slopes spanned a range ofvery flat (i.e. close to 0) to steep, with 55% of all maximumrestitution slopes being below 1, and 13% of slopesabove 2.

Methodological considerations

The cellular properties of the ventricular wall areheterogeneous (Antzelevitch et al. 1991). Ourmeasurements were made on the epicardial surface,so we have no information from endocardium or mid-myocardium. Steep APD restitution results in a greater

Figure 4. Spatial gradients of restitution with a central region of shallow slopeA, a fitted restitution curve from the centre of a region of steep restitution. B, restitution curves for neighbouringelectrodes along the two directions indicated on the ventricular epicardial polar plot in (C), illustrating theprogression from shallow restitution at the periphery to steep restitution at the centre of the posterior-RVmyocardium. The maximum restitution slope is indicated for each curve.

variation in APD and so in refractoriness over a givenrange of diastolic intervals. Depressed conduction resultsin a broader conduction velocity restitution curve andso in a wider range of conduction velocities over a givenrange of diastolic intervals. Therefore, APD restitutionalters the sensitivity of the wave back, whilst conductionvelocity restitution alters the sensitivity of the wave frontto small changes in diastolic interval (Qu et al. 2000).Hence, an integral part of the interpretation of APDrestitution is conduction velocity restitution. However,the interelectrode distance on the sock was approximately10 mm, so in view of this relatively low spatial resolution,conduction velocity restitution was not quantified in thisstudy.

The variation in pacing site between patients mayhave contributed to the interpatient variability owingto tissue anisotropy, since the latter has been shown toinfluence repolarization (Gotoh et al. 1997; Furukawaet al. 2000). However, this would not have altered theoverall findings of spatial heterogeneity within individualhearts. Comparison of hearts for which the pacing siteswere similar did not reveal any topographical similaritiesbetween hearts (data not shown).

At some electrode sites, we observed ARI restitutiondata that exhibited a non-monotonic (e.g. triphasic)relationship at short DIs, as reported in some studies(Franz et al. 1988; Morgan et al. 1992). However, this wasseen infrequently in our data, occurring for less than 2% ofthe 2885 restitution recording sites across all 14 patients.This was despite spanning the range of DIs over whichthis pattern has been observed (i.e. between approximately50 and 100 ms) and changing the S1–S2 pacing intervalby small (5 ms) decrements over this range. Reasons forthis discrepancy in restitution shape are not clear, butmay relate to endocardial-to-epicardial differences. In aprevious study of APD restitution on the endocardiumusing single site recordings, the curves were moreangulated and did not always follow a mono-exponentialtime course (Taggart et al. 2003). For these curves, weused piecewise linear regression to measure the maximumslope. In the present study, the curves were smooth, and weused a mono-exponential fit, which has the advantage ofbeing in line with the majority of other published reports.We found that the mono-exponential function providedan accurate fit to the vast majority of our data, with smallroot-mean-squared errors and no consistent pattern tothe errors between the recorded data and fitted restitutioncurves.





APD restitution slopes

Previous estimates of the restitution slope in humans haverelied on studies reporting a limited number of singleor paired site recordings (e.g. Franz et al. 1988; Morganet al. 1992; Taggart et al. 2003; Pak et al. 2004). Our datausing multi-electrode recording over the complete left andright ventricular epicardium provides a global map ofAPD restitution for low risk cardiac patients. A strikingfeature was the spatial heterogeneity of slope in all patients,with multiple gradients between numerous adjacentregions with widely disparate slopes. This is consistentwith the non-uniformity seen in some animal models,such as a single apex-to-base gradient in the guinea-pig(Pastore et al. 1999). However, the apex-to-base restitutiongradient in guinea-pig hearts is characteristically smoothand contrasts with the multiple gradients we observed.Thus no heart could be described as having either steepor flat restitution, since regions of each were present in allhearts studied.

In the present studies, a relatively high proportion(45%) of electrode sites had restitution slopes > 1.There was no obvious relationship between steepnessand pathology (such as infarction) in any individualpatient. Overall, slopes were steeper than those recentlyreported by Yue et al. (2005) on human endocardiumusing non-contact mapping in patients undergoingelectrophysiological procedures for supraventriculararrhythmias. In their study, mean restitution slopes of0.93 ± 0.49 in left ventricle and 0.65 ± 0.26 in rightventricle were observed. In our previous studies usingsingle site monophasic action potential recordings fromright ventricular endocardium (Taggart et al. 2003), weobserved mean restitution slopes of 1.05 ± 0.09 and0.71 ± 0.05 at cycle lengths of 600 and 400 ms, respectively.In another study by Pak et al. (2004) using monophasicaction potential recordings in patients at high riskof ventricular arrhythmia, restitution slopes from theright ventricular endocardium were considerably steeper(2.7 ± 1.9 and 1.9 ± 1.2 at the RV outflow tract andRV apex, respectively). The reason for the steeper slopeswe observed compared to those of Yue et al. (2005)and and compared to our own previous observationsis not clear. Possible explanations include endocardialversus epicardial differences, differences intrinsic to thepatient populations, different basic cycle lengths, andthe methodology employed for calculating the slope (amono-exponential fit was used in the present study,whereas piecewise linear regression was used in our

Figure 5. Spatial gradients of restitution with a central region of steep slopeA, a fitted restitution curve from the centre of a region of shallow restitution. B, restitution curves for neighbouringelectrodes along the two directions indicated on the ventricular epicardial polar plot in (C), illustrating theprogression from shallow restitution at the periphery to steep restitution at the centre of the LV. The maximumrestitution slope is indicated for each curve.

A

B

0

5

10

15

20

0-100 100-200 200-300 300-400

DI Range (ms)

AR

I d

isp

ers

ion

(C

OV

%)

10

12

14

16

18

0 0.5 1 1.5 2 2.5

Maximum Restitution Slope

AR

I d

isp

ers

ion

(C

OV

%)

Figure 6. Relationship between ARI dispersion and restitutionA, dispersion of activation–recovery intervals (ARI), estimated using thecoefficient of variation (COV), was greater at short cycle lengths in therange of diastolic intervals (DIs) of 0–100 and 100–200 ms comparedto that at longer DIs of 200–300 and 300–400 ms. B, plot of ARIdispersion (COV) maximum restitution slope showing a positive linearrelation between the steepness of the slope and dispersion of ARIs.

previous study and that of Yue et al. 2005). A recentstudy by Koller et al. (2005) showed that the steepportion of the dynamic restitution curve was shifted tothe right in patients with structural heart disease, andthat alternans occurred over a wider range of diastolicintervals compared to control subjects. This suggests theimportance of restitution parameters other than slope perse in mechanisms underlying arrhythmogenesis.

Overall, the restitution slope was steeper in the leftventricle compared to the right ventricle, as has beenreported by others in a guinea-pig model (Laurita et al.1996) and recently in humans (Yue et al. 2005). The slopewas flatter in patients with CAD compared to those withAVD. Several mechanisms may be contributory. Acuteischaemia has been shown to flatten APD restitution in



Figure 7. Properties of the modelAPD (A) and CV restitution (B) measured in a thin strip of uniformtissue, for each variant of the model. C, geometrical arrangement ofthe model. We simulated action potential propagation in a 2-D tissue

animal (Dilly & Lab, 1988) and human hearts (Taggartet al. 1996). In our studies, there was no evidence ofischaemia on the standard ECG, on the routine monitorsor on the epicardial electrograms. None of the patientswere known to have angina at rest or fluctuating ECGST segment changes. Nevertheless, the possibility of aneffect of ischaemia on restitution, particularly in patientswith CAD with critical stenoses, cannot be excluded.Medication with β-blockers or calcium antagonists takenby the CAD patients could have contributed significantlyto this result, since both drugs flatten restitution (Weisset al. 1999; Taggart et al. 2003). β-Blockers may also beexpected to reduce ARI dispersion.

Modelling studies suggest that, as well as the steepnessof the restitution curve, the range of diastolic intervalsover which the curve remains steep is important (Qu et al.1999). A slope that is steep over a larger portion of thecurve is more profibrillatory than one that is steep overonly a short section of the curve (Qu et al. 1999). In ourstudies, the range of diastolic intervals over which a curvewith a slope steeper than 1 remains steeper than 1 was alsoregionally distributed (Fig. 3).

Why the regionality?

The reason for the striking pattern of spatial heterogeneityof restitution slope seen in this human study is notclear. There was no obvious anatomical orientation, andthe topographical pattern was different between patients.Acute ischaemia flattens the APD restitution curve (Dilly &Lab, 1988; Taggart et al. 1996), but is unlikely to have playedmore than a minor role for reasons mentioned above, andalso because similar characteristics were observed for theAVD patients, for whom no haemodynamically significantcoronary artery narrowing was present. Cooling prolongsAPD and steepens APD restitution (Bjornstad et al. 1993);therefore, local variations in epicardial temperature couldhave influenced our results. However, we consider this alsoto be an unlikely explanation for the regionality of APDand restitution slope we observed, since we have previouslyshown that just prior to bypass the epicardial temperaturedrop was less than 1◦C and was uniform (Taggart et al.1988).

Differences in restitution properties in the RV havebeen reported between patients with RV disease andischaemic heart disease (Morgan et al. 1992). Sincespatial variation in restitution kinetics is thought tobe governed by regional differences in ion channel

sheet, with a stimulus electrode located along the bottom edge.Within the sheet was a circular region with radius R (50, 25 and12.5 mm), which was allocated different APD restitution propertiesfrom the surrounding tissue.



density, one possible explanation for the heterogeneityon the global scale that we observed may be theresult of remodelling. A possible mechanism, albeitspeculative, is the effect of altered myocardial stress–strain relations acting through mechano-electric feed-back, whereby changes in mechanical stretch alter thelocal electrophysiology (Lab, 2004; Nash & Panfilov, 2004).Ischaemia is well known to alter local ventricular wallmotion and thus regional stretch. Hypertrophy in patientswith AVD is also known to alter local stretch forces.Mechano-electric feedback in response to altered stretchmay influence ion channel behaviour and in the longerterm ion channel density (Meghji et al. 1997). The widelyvarying location of the ischaemic territory and the differingpatterns of hypertrophy in these patients provide a likelybasis for the interpatient variability of restitution slopesseen in our data.

Figure 8. Example of wavebreak and re-entryA, snapshots showing distributions of membrane potential in the model 400, 500, 600 and 700 ms after delivery ofS1 stimulus. The S1–S2 interval was 200 ms, and the S2–S3 interval was 120 ms. Resting tissue is coloured black,and the greyscale shows the extent of tissue depolarization. Dotted grey lines enclose the region with Steep2restitution, and direction of propagation is from bottom to top of each snapshot, as indicated by grey arrows.B, APD restitution curves for each region. Dashed lines show the APD of the S2 action potential in each region.C, recordings of membrane potential from sites located in each region. See text for details.

Implications

Steepness of the restitution slope. Experimental andmodelling studies have demonstrated that steeply slopedAPD restitution creates electrical instability and isprofibrillatory (Nolasco & Dahlen, 1968; Karma, 1994;Gilmour & Chialvo, 1999; Weiss et al. 1999; Garfinkel et al.2000). The original restitution hypothesis predicts that arestitution slope steeper than 1 may result in wavebreak,whereas at slopes below 1 wavebreak does not occur.

Modelling initiation and stability of re-entry intissue with heterogeneous restitution. Computationalmodels are a valuable tool for exploring the propertiesand behaviour of cardiac tissue. We have used a much-simplified computational model of action potentialpropagation to investigate the arrhythmogenic potentialof heterogeneous restitution. In a detailed and systematic



study (Clayton & Taggart, 2005), we have shown that theinteraction of a premature beat (S2) with heterogeneousrestitution acts to produce regional differences in recovery,which block an additional premature beat (S3), resultingin wavebreak and re-entry. These observations are inagreement with experimental studies (Laurita et al. 1996,1998), which showed that a premature stimulus couldproduce regional differences in recovery. An importantfeature of this finding is that wavebreak and re-entrycan be produced by this mechanism for tissue with bothsteep (slope > 1) and shallow (slope < 1) APD restitution(Clayton & Taggart, 2005). As well as influencingthe initiation of re-entry, we have also shown thatheterogeneous restitution can influence the stability of re-entry. Our preliminary results presented in Fig. 9 suggestthat the location of the tip of the re-entrant wave playsan important role, with other factors, including the sizeof the heterogeneity and the meander pattern of the tip,contributing to the stability. More detailed studies areneeded to understand how these components interact,

Figure 9. Snapshots showing stability of re-entry in both uniform and heterogeneous tissueThe greyscale in each snapshot is the same as in Fig. 8. A, unstable re-entry in a uniform model with Steep1restitution. B, stable re-entry in a uniform model with Steep2 restitution. C, unstable re-entry in heterogeneoustissue with a large region (R = 50 mm) of Steep1 restitution enclosed by tissue with Steep2 restitution. D, stablere-entry in heterogeneous tissue with a smaller region (R = 12.5 mm) of Steep1 restitution enclosed by tissue withSteep2 restitution.

because stability may also be moderated by propagationof action potentials far from the tip of a re-entrant wave(Fenton et al. 2002). However, our overall finding, thatheterogeneity is important for stability, is in agreementwith those of others who have simulated the behaviourof re-entry in heterogeneous atrial tissue (Vigmond et al.2004; Zou et al. 2005).

Limitations of the modelling. In the modelling partof this study, we chose to use a greatly simplified modelof cardiac tissue. The model had an APD of around145 ms at long DI. Although this is around 100 msshorter than the APDs observed in the experimentalpart of this study, the key idea behind the modellingstudy is that regional differences in APD restitutionare arrhythmogenic, and we have shown elsewhere thatthis mechanism is independent both of APD and ofAPD restitution slope (Clayton & Taggart, 2005). In ourmodel, we imposed sharp boundaries between regionswith different APD restitution. In real tissue, boundaries



arising from regional differences in ion channel expressionor remodelling are likely to be smooth, and further studiesare needed to examine how smooth boundaries couldaffect the initiation and stability of re-entry. In addition,we used a simplified model of membrane excitability, oursimulations were limited to a 2-D tissue sheet, and weneglected the effects of tissue contraction.

Although these simplifications do limit the extentto which the findings of the modelling study canbe applied to the human heart, this approach wasvaluable because it enabled us to study how a singlemechanism (heterogeneous APD restitution) influencesthe initiation and stability of re-entry in isolation. Thepresent study therefore illustrates the value of combininga carefully chosen computational model with experiment.The experiments showed that APD restitution propertiesin the human heart are spatially heterogeneous. Thecomputer modelling studies showed that the juxtapositionof restitution curves with different slopes facilitatedwavebreak and degeneration of VT to VF irrespectiveof whether the steepness of the slopes was greater than1 or less than 1. Thus, although recent interest in thearrhythmogenic potential of APD restitution has focusedon whether the slope is greater or less than 1 (a slopeof greater than 1 being considered profibrillatory, andless than 1 tending to stabilize re-entrant rotors), thecombined modelling and observational data suggest thatspatial heterogeneity may be of equal importance to theAPD restitution slope. Whilst providing observationaldata on human heart electrophysiology, our experimentson their own do not elucidate the mechanisms ofarrhythmogenesis. Moreover, the computer modelling inthe absence of the clinical profile would have limited value.However, their combination provides a step forwardsin our understanding of arrhythmogenesis in humanhearts.

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Acknowledgements

We gratefully acknowledge the financial support of the

Wellcome Trust, the University of Auckland’s Vice Chancellor’s

University Development Fund and the British Heart Foundation

(PG/03/102/15852).


Whole heart action potential duration restitution properties in cardiac patients: a combined clinical and modelling study

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